There exists a frequently used class of second order filter that are widely used because of their simplicity of construction and their ease of biasing. such a second order filter typically includes two storage devices for example, capacitors and inductors, a transconductance gain amplifier and resistors wherein the cut off frequency of the filter is a function of the storage devices, the resistors and the transconductance of the gain amplifier. However, the disadvantage of such a structure is that if the resistors used are on-chip, there will be a larger variation in the cut off frequency due to large absolute changes of the resistors and changes due to temperature variations since the on-chip resistors typically have a large temperature coefficient.
The traditional way of overcoming these problems is to build a reference filter and an accurate oscillator wherein the oscillator drives the filter at the correct frequency and a phase locked loop tunes the center frequency of the reference filter by varying the transconductance of the gain stage. The other filters in the system are then tracked with the reference filter. However, there are several problems with this approach. First, an expensive external component is required. Second, extra pins are required. Third, mismatches can cause errors of up to 3%.
Hence, there exists a need to provide an improved second order filter for removing the effects of on chip resistors thereby substantially reducing absolute changes in the cut off frequency of the filter.